D-type Gaussian

IG and 6-3IG. These are commonly used split-valence plus polarization basis sets. These basis sets contain inner-shell functions, written as a linear combination of six Gaussians, and two valence shells, represented by three and one Gaussian primitives, respectively (noted as 6-3IG). When a set of six d-type Gaussian primitives is added to each heavy atom and a single set of Gaussian p-type functions to each hydrogen atom, this is noted as and... 

G The 3-21G Basis Set supplemented by d-type Gaussians for each second-row and heavier main-group elements only. 3-2IG is a supplemented Split-Valence Basis Set. 

IG, 6-3IG. The 6-3IG Basis Set in which non-hydrogen atoms are supplemented by d-type Gaussians and (for 6-3IG ) hydrogen atoms are supplemented by p-type Gaussians (Polarization Functions). 6-3IG and 6-3IG are Polarization Basis Sets. 

The erivative of a p-function can thus be written in terms of an s- and a d-type Gaussian function, t he one- and two-electron integrals involving derivatives of basis functions are... 

According to Pople s nomenclature the polarized basis sets are denoted by adding a superscript asterisk to the basis set, e.g. the popular 6-31G 34 [other authors prefer the notation 6-31G(d)]. When p-orbitals are added to H as well, a second asterisk is added (e.g. 6-31G )34. The first basis set developed in this series for third-row elements, STO-3G 35, was only partially polarized, i.e., it included polarization functions (5 pure d-type Gaussians) only on third-row elements, e.g. Si, but not on second-row elements. This basis set was later replaced by the 3-21G( basis set (parentheses around the asterisk indicate that only third-row elements are augmented by d-functions)36. Both STO-3G and 3-21G(, t) should not be viewed as full polarized basis sets. The philosophy in using these half-polarized basis sets is similar to that used in going from a dz to a sv basis set. Thus, polarization functions are added only on the atoms for which it is believed that they play a larger role. This tactic may be helpful in cases where calculations with a fully polarized basis set are not feasible. 

The use of polarisation basis functions is indicated by an asterisk ( ). Thus, 6-31G refers to a 6-31G basis set with polarisation functions on the heavy (i.e. non-hydrogen) atoms. Two asterisks (e.g. 6-31G ) indicate the use of polarisation (i.e. p) functions on hydrogen and helium. The 6-31G basis set is particularly useful where hydrogen acts as a bridging atom. Partial polarisation basis sets have also been developed. For example, the 3-21G basis set has the same set of Gaussians as the 3-21G basis set (i.e. three functions for the inner shell, two contracted functions and one diffuse function for the valence shell) supplemented by six d-type Gaussians for the second-row elements. This basis set therefore attempts to account for d-orbital effects in molecules containing second-row elements. There are no special polarisation functions on first-row elements, which are described by the 3-21G basis set. 

For second-row atoms, d orbitals contribute significantly to the bonding. To allow for this, the 3-21G basis set (defined for H through Ar) is constructed by the addition to the 3-21G set of a set of six d-type Gaussian functions on each second-row atom. For H-Ne, the 3-21G set (which is sometimes called 3-21G ) is the same as the 3-21G set. 

IG [the 6-31G basis set augmented with six d-type gaussian primitives on each heavy (Z > 2) atom, to permit polarization]... 

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